FOOT: an experiment to measure fragmentation cross sections for hadrontherapy - Monte Carlo data analysis and preliminary results from GSI and CNAO data taking

SCUOLA DI SCIENZE

Corso di Laurea Magistrale in Fisica

FOOT: an experiment to measure

fragmentation cross sections for

hadrontherapy

Monte Carlo data analysis and preliminary results from GSI and CNAO data taking

Relatore:

Chiar.ma Prof.ssa

Gabriella Sartorelli

Correlatore:

Dott. Roberto Spighi

Presentata da:

Andrea Ubezio

Hadrontherapy is a cancer treatment that exploits the irradiation with heavy charged particles. Its main advantage derives from the depth-dose profile of this particles, which release most of their energy in a narrow region inside the patient body. One of the major problem of hadrontherapy is the nuclear fragmentation, which is not a fully understood phenomenon. The main goal of the FOOT experiment is to study the fragmentation of heavy-ion beams onto H-enriched targets in order to identify the produced fragments and to measure the differential cross sections of such processes of relevant interest for hadrontherapy. The use of the inverse kinematic approach should provide important information to better understand the effect of the proton/hadron therapy on patient tissues. The FOOT detector has been designed to perform high-precision identification of the produced fragments by measuring their trajectory, velocity, momentum and ener-gy. Monte Carlo simulations and test beams are ongoing in order to verify the detector capability. In this thesis, an analysis of Monte Carlo data has been carried out in order to show the FOOT capability in identifying fragments and reconstructing the fragmen-tation cross sections. The data taking performed at the GSI has been also studied; the preliminary results confirm, in agreement with Monte Carlo data, an excellent precision in charge identification.

L’adroterapia è un trattamento antitumorale che sfrutta l’irraggiamento con particelle cariche pesanti (adroni). Il vantaggio principale di questa tecnica deriva dalla particolare interazione delle particelle adroniche con la materia, le quali rilasciano la maggior parte della loro energia in una regione ristretta all’interno del corpo del paziente. Uno dei maggiori problemi dell’adroterapia è il fenomeno della frammentazione nucleare, il quale non è ancora del tutto compreso. L’esperimento FOOT ha come obiettivo lo studio di di processi di frammentazione che interessano l’adroterapia, sfruttando le collisioni tra fasci di particelle cariche pesanti su target contenenti idrogeno e misurandone le sezioni d’urto. L’utilizzo della cinematica inversa permette di comprendere meglio la frammentazione nucleare e gli effetti che essa può produrre sui tessuti del paziente. Il rivelatore di FOOT è stato progettato per identificare i frammenti nucleari con precisione elevata, essendo in grado di misurarne traccia, velocità, quantità di moto ed energia. Simulazioni di Monte Carlo e test beam sono in corso per verificare le performance del rivelatore. In questa tesi viene discussa un’analisi di dati di Monte Carlo al fine di mostrare le capacità di FOOT nell’identificare i frammenti e ricostruire le sezioni d’urto di frammentazione. Un’altra analisi coinvolge i dati raccolti presso il GSI; i risultati preliminari confermano, in accordo con i dati Monte Carlo, un’eccellente precisione nell’identificazione della carica dei frammenti.

Abstract i

Sommario ii

Introduction 1

1 Hadrontherapy 3

1.1 Physical principles . . . 3

1.1.1 The Bethe-Bloch formula . . . 4

1.1.2 Bragg peak and range of the particles . . . 7

1.1.3 Nuclear fragmentation . . . 11

1.2 Radiobiological considerations . . . 14

1.2.1 Dosimetric quantities . . . 14

1.2.2 Biological effects of radiation . . . 15

1.2.3 LET and RBE . . . 17

1.2.4 Oxygen Enhancement Ratio . . . 20

1.2.5 Cell survival curve . . . 21

1.3 Treatments with heavy charged particle . . . 25

1.3.1 History of hadrontherapy . . . 25

1.3.2 Proton therapy . . . 27

1.3.3 Ion therapy . . . 34

1.3.4 Other particle therapies . . . 38

2 The FOOT experiment 42

2.1 Motivations and aims . . . 43

2.2 Experimental setup . . . 46

2.2.1 Design Criteria . . . 46

2.2.2 Electronic setup for heavy fragment detection . . . 48

2.2.3 Emulsion setup for light fragments detection . . . 63

2.3 Inverse kinematic approach . . . 70

2.4 DAQ and trigger . . . 72

3 Monte Carlo Data Analysis 75 3.1 Charge identification . . . 76

3.2 Mass identification . . . 81

3.2.1 Mass reconstruction methods . . . 81

3.2.2 χ2 _{and ALM fit . . . . 88}

3.3 Cross section calculation . . . 95

3.3.1 Background evaluation . . . 98

3.3.2 Unfolding . . . 100

3.3.3 Efficiency . . . 105

3.3.4 Fragmentation cross sections and FLUKA cross sections comparison105 4 GSI data analysis 118 4.1 Scintillator calibration and performance . . . 119

4.1.1 ToF system calibration and Z reconstruction . . . 125

4.2 Fragmentation measurement . . . 131

4.2.1 CNAO calibration and Z identification . . . 134

Conclusions 138

A General information about cross section 140

B Analysis of data from 16O (200 MeV/u) on C target 142

C Comparison of differential cross sections and FLUKA differential cross

1.1 Mass stopping power in function of βγ. In each plot one can see a β−2 trend at low momenta, a minimum when β ∼ 0.96 and an increase at higher β values (relativistic rise). . . 6 1.2 Bragg curve for protons in relative stopping power; the plot shows the

sharp deposition of energy known as the Bragg peak[5]. . . 8 1.3 (a) Relative fraction of the fluence in a heavy charged particle beam

as a function of depth in the Continuous-Slowing-Down Approximation (CSDA). (b) A more realistic behaviour of the fluence: not all particles stop at the same depth, we can see the range distribution known as range straggling. . . 9 1.4 Mean range as a function of initial kinetic energy. The plot shows values

related to different ions in water [7]. . . 11 1.5 A simplified model of the nuclear fragmentation due to peripheral

colli-sions of projectile and target nucleus [13]. . . 13 1.6 RBE as a function of LET. The diagram illustrates why radiation with

a LET of 100 keV/µm has the greatest RBE: for this LET, the average separation between ionizing events coincides with the diameter of the DNA double helix (i.e., about 2 nm). Radiation of this quality is most likely to produce a double-strand break from one track for a given absorbed dose [17]. . . 18 1.7 Comparison between different particles RBE curves as functions of LET

[18]. . . 19

1.8 Oxygen enhancement ratio (OER) as a function of Linear Energy Transfer (LET). The vertical line (LET = 10 keV/µm) separates low-LET values from high-LET values [21]. . . 21 1.9 ionization and free radicals formation induced by high-LET and low-LET

radiations. In a high-LET regime, subsequent ionizations are separated by a distance of about 102_-103_{pm, while the formation of the H}• _radical

occurs about 15 nm away from the primary ionization process; in this case, the OH• + OH• recombination (that produce hydrogen peroxide) is favoured. In a low-LET regime, ionizations occur every tens of nm, thus OH• and H• couples are closer than two OH• radicals, then their recombination (that produce H2O) is favoured. . . 22

1.10 Ionization density in a medium irradiated by X-rays (a) and high LET particles (b). The small circles represent biological targets and the dots represent ionizations produced along the tracks [22] . . . 23 1.11 Cell survival as a function of dose for densely and sparsely ionizing

ra-diation. The fraction of cells surviving is plotted on a logarithmic scale against dose on a linear scale [25]. . . 24 1.12 Representation of the RBE as the ratio between dose values from

diffe-rent radiation given a fixed surviving fraction value. According to linear quadratic model, RBE is maximal when dose → 0. If the fractional dose increases, the RBE converges to a minimal value [27]. . . 25 1.13 Absorbed dose D as a function of depth z in water from an unmodulated

(pristine) proton Bragg peak produced by a broad proton beam with an initial energy of 154 MeV. The various regions that are labeled are defined in the text. Note that the electronic buildup region, which spans only a few millimeters, is not visible in this plot. This type of dose distribution is clinically useful because of the relatively low doses delivered to normal tissues in the sub-peak and distal-falloff regions with respect to the target dose delivered by the peak [29]. . . 28

1.14 (a) Proton fluence I(0, x) along the beam central axis as a function of the depth x in water. Curves are shown for beams with circular cross sec-tions with radius between 1 and 4 mm. Some protons are lost because of scattering events that deflect them from the central axis. This is increasin-gly observed for small beams and at large depths. (b) The corresponding central-axis absorbed-dose curves. Note how the fluence depletion reduces the absorbed dose at the peak with respect to the entrance dose [30]. . . 30 1.15 Absorbed dose D as a function of depth z in water from a spread-out

Bragg peak (SOBP) (uppermost curve) and its constituent pristine Bragg peaks (lower curves; for clarity, all but the deepest pristine Bragg peak are only partly drawn). In many cases, the clinical target volume is larger than the width of a pristine Bragg peak. By appropriately modulating the proton range and fluence of pristine peaks, the extent of the high-dose region can be widened to cover the target volume with a uniform dose [29]. 31 1.16 Absorbed dose D as a function of depth z in water from a spread-out

proton Bragg peak (SOBP). Various locations and regions that are indi-cated on the plot are defined in the text. Note that the electronic buildup region, which spans only a few millimeters, is not visible in this plot [29]. 32 1.17 The total proton-induced non-elastic nuclear reaction cross section in

oxygen versus proton energy, showing a threshold corresponding to the Coulomb barrier at approximately 6 MeV [31]. . . 33 1.18 Measured Bragg curves of 12_{C ions stopping in water [51]. . . . 36}

1.19 Bragg curve for 670 MeV/u 20_{Ne ions in water measured at GSI}

(cir-cles) and calculated contributions of primary ions, secondary and tertiary fragments [52]. . . 37 1.20 Cross-section for photon scattering from carbon showing the

contribu-tions of photoelectric, elastic (Rayleigh), inelastic (Compton) and pair-production cross sections to the total cross sections. Also shown are the experimental data (open circles). The energy of photons used in conventional radiotherapy starts from few tens of keV up to ∼ 10 MeV [54]. . . 39

1.21 Depth-dose distributions from X-rays, proton beams, and carbon ion beams

superimposed with each other for comparison [55]. . . 40

2.1 illustrative image of the expected relative impact of the target fragmen-tation in the entrance and in the peak regions as compared to the effect of the inactivation by ionization [61]. . . 43

2.2 Full spectra of fragments from target media in the case of a prostate irradiation with protons of 160 MeV, integrated in the complete range of beam propagation [63]. . . 44

2.3 Schematic view of the FOOT electronic setup [69]. . . 49

2.4 Picture of the Start Counter mechanical frame. . . 50

2.5 Technical draw of the beam monitor [69]. . . 51

2.6 Photo of the inside of the Beam Monitor. . . 52

2.7 3D model of the two magnets in Halbach configuration designed for the magnetic spectrometer [69]. . . 53

2.8 Magnetic field intensity B as a function of z along the beam central axis (x = y = 0). The plot shows the double gaussian trend produced by two separated Halbach magnets (simulation performed with the OPERA code version 16R1) [69]. . . 54

2.9 Target and vertex tracker geometrical scheme (left) and a M28 pixel sensor picture (right) [69]. . . 55

2.10 Upper left and right panel: beam profile in the two M28 sensors (units on both axes are in µm). Bottom panel: reconstructed angular divergence of the beam in mrad [69]. . . 56

2.11 Inner tracker scheme. On the right we see how the four modules are located in the global structure. Each module has two connectors, in red and green color, respectively on the front and back side of the ladder [69]. 57 2.12 Picture of a MSD layer prototype. . . 58

2.13 Picture of a SCN bar prototype (left) and the entire scintillator (right). . 59

2.14 STC-SCN measurement of the time of flight performed at the GSI test beam (April 2019) with the electronic setup. The standard deviation of the fitted distribution (boxed in red) represents the time resolution. . . . 60

2.15 Schematic view of the CAL crystals setup. . . 61 2.16 Energy resolution of the BGO crystals as a function of energy for different

particle beams obtained at GSI and CNAO. . . 62 2.17 Emulsion spectrometer setup inside the FOOT detector [69]. . . 64 2.18 Schematic overview of the ECC layout (not to scale) [69] (è quello di

OPERA?). . . 65 2.19 Scheme of the ES Section 1: vertex and tracking detector [69]. . . 66 2.20 Scheme of ES section 2: charge identification detector. . . 67 2.21 Scheme of ES section 3 dedicated to the momentum measurement [69]. . 67 2.22 Scheme of the tracks reconstruction: a micro-track consists of a sequence of

aligned clusters in one of the two layers (top or bottom), while a base-track is constituted by geometrically aligned top and bottom micro-tracks. [69]. 68

3.1 Energy resolution in the scintillator as a function of the energy deposition of the fragment. . . 78 3.2 Time resolution as a function of the fragment charge. . . 79 3.3 Charge number Z of fragments produced in the fragmentation in linear

scale (a) and in logarithmic y scale (b). The element relating to the charge peak is indicated in blue. . . 80 3.4 Mass numbers A1 from 1 to 16 reconstructed with the ToF and momentum

measurement. . . 84 3.5 Mass numbers A2 from 1 to 16 reconstructed with the kinetic energy and

momentum measurement. . . 85 3.6 Mass numbers A3 from 1 to 16 reconstructed with the ToF and kinetic

energy. . . 86 3.7 Distribution of the ratio between the measured kinetic energy (energy

deposition in the scintillator plus energy deposition in the calorimeter) and the true kinetic energy (generated in the simulation) of the fragments produced in the fragmentation reaction16_{O + C}

2H4. . . 89

3.8 Mass numbers distributions obtained with the standard χ2 _minimization

3.9 Cutted distributions (χ2 _{< 5 events only) of the mass number obtained}

with the standard χ2 minimization method. . . 92 3.10 Mass resolution as a function of the mass number obtained with different

mass reconstruction methods. . . 94 3.11 Mass number of carbon fragments in different kinetic energy range. . . . 97 3.12 Migration histograms for the background evaluation of carbon fragments

in different kinetic energy ranges. . . 99 3.13 Production yields (blue lines) and background events (red lines) as a

function of kinetic energy of carbon isotopes. . . 101 3.14 Production yields background subtracted as a function of kinetic energy

of carbon isotopes. . . 102 3.15 Migration histograms of kinetic energy used in the unfolding procedure. . 103 3.16 Distributions of yields background subtracted (violet) and unfolded

distri-butions (green) with respect to kinetic energy of carbon isotopes. . . 104 3.17 Reconstruction efficiency as a function of kinetic energy of each carbon

isotope. . . 106 3.18 Energy differential cross section for the production of carbon isotopes in

fragmentation reaction induced by a 200 MeV/u oxygen-16 beam impin-ging on a C2H4 target. . . 108

3.19 Energy differential cross section for the production of carbon isotopes in fragmentation reaction induced by a 200 MeV/u oxygen-16 beam impin-ging on a C target. . . 110 3.20 Energy differential cross section for the production of carbon isotopes in

fragmentation reaction induced by a 200 MeV/u oxygen-16 beam impin-ging on a H target. . . 112 3.21 Ratio between the reconstructed total number of fragments for each

car-bon isotope and the total number of fragments generated in the simulation (16_{O on C}

2H4). . . 114

3.22 Ratio between the reconstructed total number of fragment for each carbon isotope and the total number of fragments generated in the simulation (16_O

3.23 Comparison between the energy differential cross sections obtained in this analysis (blue) and the FLUKA cross sections used in the MC simula-tion (red), relating to the producsimula-tion of12C fragments in different targets (C2H4, C and H). . . 116

4.1 Schematic view of the electronic setup used at the GSI test beam. . . . 118 4.2 Schematic view of the scintillator used at the GSI test beam. The

hi-ghlighted bars are those that have been calibrated at GSI with a 400 MeV 16-oxygen beam. . . 119 4.3 Mean collected charge at the two ends of a scintillating bar as a function

of the position, for a proton beam with the fixed energy of 170 MeV. The 0 position represent the center of the bar. Solid lines represent the fit to the data with eq. 4.2 [91]. . . 120 4.4 Scheme of the scintillator bar read-out. A signal charge independent by

the particle hit position can be obtained by multiplying the signal charge at the left end (Qleft) by the signal charge at the right end (Qright). . . . 121

4.5 (a) Distributions of signal charge from bar 11 and bar 14 of the rear layer of the scintillator obtained with 16_{O particles (400 MeV/u); F}

eq is

the equalisation factor. (b) Same distributions after equalisation. The equalisation value has been arbitrarily chosen equal to 70. . . 122 4.6 Distributions of equalised signal charge from bar 14 of the rear layer. . . 122 4.7 Energy deposited by16O particles (400 MeV/u) in the bar 14 of the

scin-tillator. . . 123 4.8 Distribution of the signal charge from the scintillator obtained with a

400 MeV/u16_{O beam. The signal charge of each event is given by the sum}

of the charge collected in the two layers. . . 125 4.9 Distribution of time measured with the bar 14 of the rear layer of the

scintillator before (a) and after the equalisation (b). This distribution has been obtained by detecting only 16_{O (400 MeV/u) particles coming from}

the test beam. 10.44 ns is the time that a beam particle takes to travel from the Start Countuer to the scintillator; all the bars has been equalised at this time by subtracting the corresponding time offset. . . 126

4.10 Distribution of time of flight of beam particles from the intended target position to the scintillator. This time measurement has been obtained as the mean value of the times measured by the two layer of the scintillator. 127 4.11 Z Distribution obtained with the energy loss and the ToF measured by

the bar 14 of the scintillator. . . 129 4.12 Distribution of the charge Z obtained from the scintillator measurements

performed on 400 MeV/u16O particles. . . 131 4.13 Scheme of the ghosting phenomenon in the scintillator: two impinging

fragments produce four bar intersections, as the detector has been hit by four particles. . . 132 4.14 (a) Distribution of the signal charge from the scintillator obtained with

fragmentation events induced by16_{O (400 MeV/u) impinging on a C}

tar-get. (b) Same distribution, but in linear scale; the oxygen peak has not been included in order to better appreciate the other peaks. . . 133 4.15 Calibration of three scintillator bars. (a) Calibration performed at CNAO

with proton and carbon beams. (b) Calibration performed with CNAO and GSI data from proton, carbon and oxygen beams. (c) Calibration performed with CNAO and GSI data; the oxygen point is not in agreement with the other data, therefore it is not included in the fit. . . 135 4.16 Charge Z of the fragments produced at the GSI data taking by using a

400 MeV/u 16O beam impinging on a C target. . . 136

B.1 Charge Z distributions of fragments produced in the fragmentation. . . . 143 B.2 Charge Z distributions of fragments produced in the fragmentation in

logarithmic y scale. . . 143 B.3 Mass numbers A1 from 1 to 16 reconstructed with the ToF and momentum

measurement. . . 144 B.4 Mass numbers A2 from 1 to 16 reconstructed with the kinetic energy and

momentum measurement. . . 145 B.5 Mass numbers A3 from 1 to 16 reconstructed with the ToF and kinetic

B.6 Mass number distributions obtained with the standard χ2 _minimization

method. . . 147 B.7 Cutted distributions (χ2 < 5 events only) of the mass number obtained

with the standard χ2 _{minimization method. . . . 148}

B.8 Mass resolution as a function of the mass number obtained with different mass reconstruction methods. . . 149 B.9 Mass distributions of carbon fragments in different kinetic energy range. . 150 B.10 Migration histograms for the background evaluation of carbon fragments

indifferent energy ranges: true mass number A vs reconstructed mass number A. . . 151 B.11 Production yields (blue lines) and background events (red lines) as a

function of kinetic energy (MeV/u) of carbon isotopes. . . 152 B.12 Production yields background subtracted as a function of kinetic energy

(MeV/u) of carbon isotopes. . . 153 B.13 Migration histograms of kinetic energy (MeV) used in the unfolding

pro-cedure: true kinetic energy vs reconstructed kinetic energy. . . 154 B.14 Production yields background subtracted before (violet lines) and after

(green lines) the unfolding procedure as a function of kinetic energy (MeV/u) of carbon isotopes. . . 155 B.15 Reconstruction efficiency as a function of kinetic energy (MeV/u) of each

carbon isotope. . . 156

C.1 Differential cross section (mbarn/MeV) as a function of kinetic energy (MeV/u). The blue markers are the differential cross section found in this analysis, the red markers are the differential cross sections used in the FLUKA simulation. The plots refer to the carbon isotopes produced by an oxigen-16 beam (200 MeV/u) impinging on a C2H4 target. . . 158

C.2 Differential cross section (mbarn/MeV) as a function of kinetic energy (MeV/u). The blue markers are the differential cross section found in this analysis, the red markers are the differential cross sections used in the FLUKA simulation. The plots refer to the carbon isotopes produced by an oxigen-16 beam (200 MeV/u) impinging on a C target. . . 159

C.3 Differential cross section (mbarn/MeV) as a function of kinetic energy (MeV/u). The blue markers are the differential cross section found in this analysis, the red markers are the differential cross sections used in the FLUKA simulation. The plots refer to the carbon isotopes produced by an oxigen-16 beam (200 MeV/u) impinging on a H target. . . 160

1.1 weighting factor of different type of radiation; the weighting factor for neutrons can range from ∼ 3 up to 20 and it is given by a continuous function of the neutron energy, as discussed in [14]. . . 15

2.1 Average data for target fragments from a 180 MeV proton beam in water, estimated according to a semi-empirical formula. . . 45 2.2 Overview of the FOOT research program. PMMA refers to Poly(methyl

methacrylate) whose chemical formula is C5O2H8. . . 46

2.3 Current resolution of the detectors of the FOOT electronic setup. . . 63 2.4 DAQ components, rates and bandwidths . . . 73

3.1 List of fragments produced in a fragmentation reaction induced by an oxigen-16 beam impinging on a C2H4 target. . . 76

3.2 Scintillator characteristics included in the Bethe-Block formula for the fragment charge determination. . . 77 3.3 Mean values, standard deviations and resolutions of the charge

distribu-tions showed in fig. 3.3 . . . 80 3.4 List of the mainly produced isotopes for each charge in a fragmentation

reaction induced by an oxygen-16 beam impinging on a C2H4target.

The-se isotopes have been The-selected to study the mass identification performance of the apparatus. . . 81 3.5 Resolution of the quantity measured with the simulated FOOT apparatus. 83

3.6 Mean values, standard deviations and resolutions of the mass number distributions obtained with the three methods (A1, A2, A3) discussed in

section 3.2.1 . . . 87 3.7 Mean values, standard deviations and resolutions of the mass number

distributions obtained with the standard χ2_{-fit method (top table) and}

with the application of the χ2 _{< 5 selection (bottom table). . . . 93}

3.8 Energy ranges within which the energy differential cross section has been calculated. . . 96 3.9 Differential cross sections (mbarn/MeV) in each considered kinetic energy

range for carbon isotopes produced in the fragmentation reaction induced by16_{O beam on C}

2H4 target. . . 107

3.10 Differential cross sections (mbarn/MeV) in each considered kinetic energy range for carbon isotopes produced in the fragmentation reaction induced by16O beam on C target. . . 109 3.11 Differential cross sections (mbarn/MeV) in each considered kinetic energy

range for carbon isotopes produced in the fragmentation reaction induced by16_{O beam on H target. . . . 111}

3.12 Total production cross sections (mbarn) of carbon isotopes in fragmenta-tion processes induced by16O beam on different target. σ₁tot refers to the total cross section obtained by integrating the differential cross sections given in fig. 3.18-3.20 ; σ₂tot has been obtained with the same analysis as described in chapter 3, but performed in a single wide energy range in-cluding all the kinetic energy of the produced fragments; σtot

2 is the cross

section used in the FLUKA MC simulation. . . 117

4.1 Equalisation factors of each equalised bar of the scintillator; mean, stan-dard deviation and resolution of the related signal charge distribution obtained with a 400 MeV16O beam. . . 124 4.2 Time offset of each calibrated bar; mean, standard deviation and

resolu-tion of the ime of flight of 400 MeV 16_{O particles meausured with each}

4.3 Mean, standard deviation and resolution of Z distributions obteained from the measures performed by each scintillator bar on a 400 MeV16O beam. . 130 4.4 Energy lost inside the scintillator layers by the particles used at CNAO

for calibration. . . 134 4.5 Fit parameters of the Birks’ function for each calibrated bar of the

According to the World Health Organization, cancer is one of the most deadly diseases in the world. Nowadays, tumors are treated with different techniques, including surgery, chemotherapy, radiotherapy and immunotherapy. Radiotherapy now contributes to the treatment of about 23 % of all cancer patients, used alone or in combination with surgery, chemotherapy or immunotherapy. In addition to the well-established photon radiothera-py, in the last decade the number of patients treated with heavy charged particle beams has increased. This technique is called hadrontherapy and its main advantage derives from the depth-dose profile of charged particles, which is characterised by a low-dose entrance channel and by a following narrow region, the Bragg peak, where the maximum of the dose release is reached. The Bragg peak depth depends on the beam energy, which is tunable in the particle accelerators that provides the therapeutic beam. By matching the Bragg peak with the depth of the tumor inside the patient’s body, it is possible to affect the cancer cells and, at the same time, to preserve the surrounding healthy tissue. At present, one of the major problem of hadrontherapy is the nuclear fragmentation, which is not a fully understood phenomenon whose effects can change the dose profile: nuclear reaction inside the patient’s body may occurs, resulting in the emission of nuclear fragments, whose type and energy differ from those of primary particles. Both the projectile and the target nuclei can undergoes fragmentation: in heavy ion treatments, the fragments of the projectile (with the same velocity but with lower mass than the projectile itself) can travel farther and can deliver a non-negligible dose beyond the Bragg peak, harming the healthy tissue; in proton therapy the projectile can not fragment at therapeutic energy, but the fragmentation of target nuclei could be an issue, since low energy fragments, consequently with short range (∼ µm), are produced, resulting in a

local dose deposition which mainly involves the entrance channel.

FOOT (FragmentatiOn Of Target) is a fixed target experiment equipped with a multipurpose detector for the detection and identification of heavy charged particles. The main goal of this experiment is to fill the lack of experimental data concerning fragmentation cross sections, which are not already studied for the nuclei of the human tissue (mainly H, C and O) in the therapeutic energy range (between tens and hundreds of MeV per nucleon). The main challenge is to investigate target fragmentation processes in proton therapy, since the very short range of the emitted fragments does not allow them to escape the experimental target and, then, to be detected. In order to overcome this problem, FOOT adopts an inverse kinematic approach, which consists in switching the target and the projectile roles, so as to produce fragments with a forward boost. FOOT can also carry out studies on projectile fragmentation by exploiting the ordinary direct kinematics.

In the first chapter of this thesis, the principles of hadrontherapy and interaction of radiation with matter, with particular regard to the radiobiological aspects, are discussed. Furthermore, the nuclear fragmentation phenomenon is introduced. The second chapter describes in detail the FOOT apparatus and its components, showing the tests performed and the resolutions obtained on the various detectors. The third chapter shows an analysis performed on data from a Monte Carlo simulation of the FOOT apparatus, while in chapter 4, two data taking performed at the GSI and CNAO facilities are discussed and analysed. The purpose of this work is to develop an analysis software able to manage the data produced by the experiment, to study the detector precision in particle identification and to obtain the final cross section measurements. The analysis of real data, acquired at GSI, represent the first confirmation of the FOOT capability to detect and identify the fragments with appropriate resolution.

Hadrontherapy

Hadrontherapy is an oncological technique that uses protons and ions as projectiles in order to kill cancer cells. This therapy is particularly useful in situations in which standard treatments, like surgery, chemotherapy or the conventionally radiotherapy (that makes use of X-rays and γ-rays), cannot be used, as, for example, cancer located inside or near sensitive organs.

In this chapter the main aspects of hadrontherapy, its working principles and appli-cations are discussed.

1.1

Physical principles

In this section we will see which basic interactions occur when heavy charged particles pass through matter and what effects can be produced. Heavy charged particles (with mass M >> me, where me is the electron mass) interact with matters in terms of

electrons and nuclei, so processes that can occur are both electromagnetic and nuclear. In general, two principal electromagnetic features characterize the passage of heavy charged particles through matter: a loss of energy by the incident particle (inelastic collisions with the atomic electrons) and a deflection of the particle from its original direction (elastic scattering from nuclei). These two phenomena may occur many times in a unit path length in matter. For what concern the nuclear interactions, heavy particles may

also make strong interaction directly with nuclei. This process might produce secondary particles.

While the single particle interactions can be described at the atomic or nuclear level, at the macroscopic level the most important quantity is the stopping power that measure the energy loss per unit path length. The stopping power depends on the properties of the charged particle, such as mass, charge, velocity and energy, as well as on the properties of the absorbing medium, such as its density and atomic number.

Below in this section we will discuss the energy loss of a heavy charged particle in matter due to electromagnetic interaction, described by the Bethe-Bloch formula, and we will also see in details the nuclear fragmentation process that leads to secondary particles.

1.1.1

The Bethe-Bloch formula

The e.m. interaction represent the primary cause of energy loss of an heavy charged particle travelling in matter, in particular, this loss is mainly due to inelastic collisions with the atomic electrons. In these processes the energy transfer leads to an excita-tion (soft collision) or ionizaexcita-tion (hard collision) of the atom. The amount of energy transferred in each collision is a small fraction of the total kinetic energy of the particle, however the number of collisions per unit path length (in dense matter) is large, than a substantial cumulative energy loss could be observed.

Inelastic scattering from nuclei also occurs frequently although not as often as electron collisions. The amount of energy transferred in this way depends on the ratio between the mass of the impinging particle and the mass of the nuclei that constitute the medium. The energy lost is in any case a small fraction of the overall energy loss, since the pro-bability of nuclear scattering is much lower than the propro-bability of interactions with the electrons (the ratio between scattering cross sections is σnucleus/σatom ' 10−8 − 10−10)1.

Nevertheless, the atomic nuclei of the medium are responsible for elastic Coulomb

scat-1_{To estimate this ratio we used a classical approach that considers particles as hard spheres. In}

this way, the cross section can be obtained using the relation σnucleus(atom)= π(2rnucleus(atom))2, where

tering that are the main cause of the deflection of the incident particle with respect to its original motion.

So, during its walk through an absorbing medium, a charged particle experiences a large number of interactions before its kinetic energy is completely lost. In each interaction the charged particle may lose some of its kinetic energy and its path may be altered. The energy δE lost in a collision depends on the characteristics of the particle as well as the absorber. However, even with the same particle and medium characteristics, the energy lost δE isn’t the same in every collision, but depends on the scattering kinematics. Anyhow, we can consider a statistical quantity dE, based on the average energy loss that does not take into account the kinematics of each process.

The rate of energy loss (typically expressed in MeV) per unit of path length (typically expressed in cm) in an absorbing medium is called linear stopping power (−dE/dx) [1]. The stopping power for heavy charged particles in matter was first calculated by Bohr using a classical approach [2] and later by Bethe and Bloch using quantum mechanics [3, 4]. The formula obtained by Bethe, Bloch and other physicists is

−dE dx = 2πNAr 2 emec2ρ Z A z2 β2  ln 2meγ 2_β2_c2_W max I2  − 2β2_{− δ − 2}C Z  (1.1)

In this formula we can see a first constant term consisting of the classical electron radius (re= 2.8179403227(19)×10−13cm), the electron mass (me= 9.1093837015(28)×10−28g),

the Avogadro’s number (NA= 6.0221409 × 1023mol-1) and the speed of light in vacuum

(c = 299.792458 × 1010cm/s). Then, there is a part depending on the characteristics of the medium (atomic number Z, atomic weight A and density ρ) and a part depen-ding on beam characteristics (the charge of the incident particle z, in unit of e, and its velocity β = v/c). The logarithmic term depends on beam quantities (such as β and γ = 1/p1 − β2_{), the mean excitation potential I and the maximum energy transfer in}

a single collision Wmax.

Wmax= 2mec2β2γ2 1 + 2me Mp1 + β2γ2+ ( me M)2 (1.2)

charged particles), eq. 1.2 becomes Wmax = 2mec2β2γ2. The last two terms in eq. 1.1

represent the density effect correction δ and the shell correction C. The density effect correction is needed to take into account the polarization effect due to a charged particle travelling in a medium full of electrons. Electrons far from the particle path are shielded, so the effective dE/dx is lower. This correction increases with the density of medium density and with the beam energy. The shell correction becomes important when the energy of the incident particle is low enough to make the particle velocity comparable or lower than the electrons velocity in the medium. In this situation we can no longer assume that the electron is at rest when the interaction happens, therefore the transferred energy is slightly reduced. Both corrections are negligible in the energy range useful for hadrontherapy.

Figura 1.1: Mass stopping power in function of βγ. In each plot one can see a β−2 trend at low momenta, a minimum when β ∼ 0.96 and an increase at higher β values (relativistic rise).

is obtained. This quantity is more convenient because the unit path length is now expressed in g· cm-2 and it doesn’t depend on the density of the medium. In figure 1.1 the mass stopping power is shown as a function of the βγ value of the incident particle for different absorbing materials; one can also see the momentum scale of proton on the x axis.

For a non relativistic particle, dE/dx is dominated by the overall factor 1/β2 _and

decreases with increasing velocity until a minimum is reached at β ∼ 0.96. Particles at this minimum point are usually referred to as Minimum Ionizing Particles (MIP). As the energy increases beyond the MIP point, dE/dx also increases due to the logarithmic con-tribution in the Bethe-Bloch formula; this trend is called relativistic rise. It is important to notice that hadrotherapy uses proton beams whit kinetic energy of ∼ 0.2 GeV, which corresponds to a proton momentum of ∼ 0.66 GeV, thus, we are in the β−2-dependent region of the Beteh-Bloch.

When different projectiles with the same velocity are compared, the charge z is the only factor that changes outside the logarithmic term, so particles with greater charge have a larger specific energy loss. Instead, studying dE/dx for different materials as absorbers, it can be pointed out its main dependence on the electron density of the medium: the higher is the material density, the higher is the energy loss. If we consider the mass stopping power (as shown in fig. 1.1, there is no more dependence on the material density, thus the only factor that takes into account the properties of the material is the Z/A ratio.

Taking into account all the above considerations, it can be seen that a particle deposits much more energy when its velocity is low. This is the case of a very low energy particle or a particle near the end of its path, which has therefore lost much of its initial energy.

1.1.2

Bragg peak and range of the particles

As we saw in the previous section, a particle travelling through an absorbing medium progressively slows down, because of energy loss, as it goes deep in the material and when a particle is close to rest it releases most of its energy. Thus, we can reinterpret the Bethe-Bloch trend considering the stopping power as a function of depth.

Figura 1.2: Bragg curve for protons in relative stopping power; the plot shows the sharp deposition of energy known as the Bragg peak[5].

Figure 1.2 shows the stopping power for a proton beam with respect the crossed path, also called Bragg curve. We can easily see how the dE/dx rises at a certain travelling distance and then it decreases abruptly. This sharp region, known as Bragg peak, occurs at a specific depth, depending on the beam energy, that corresponds to the range of the beam particles. In an oncological perspective, this means that, knowing the depth of the tumor in the patient’s body, we can set the energy of the beam in order to send most of the ionization power into the tumor and protect the surrounding healthy tissue.

Later (see section 1.3.2 and 1.3.3) we will see in details some Bragg curve from different type of particle beams considering the radiobiological aspects, while below we will define the particle range and see how to find it.

The range is an important parameter because it gives information about the longi-tudinal energy transfer in the material. We can define the mean range as the average length that the particle travels inside an absorbing medium before running out of kinetic energy. Considering a monoenergetic beam, we can assume that it deposits a continuous and constant amount of energy per unit of path length equal to its stopping power. In this Continuous-Slowing-Down Approximation (CSDA), all the particles run out of

ener-gy at the same depth, equal to the CSDA range. Figure 1.3, curve (a), show this ideal behaviour in terms of fraction of beam particles as a function of depth.

Figura 1.3: (a) Relative fraction of the fluence in a heavy charged particle beam as a function of depth in the Continuous-Slowing-Down Approximation (CSDA). (b) A more realistic behaviour of the fluence: not all particles stop at the same depth, we can see the range distribution known as range straggling.

However, the energy loss undergoes statistical fluctuations, so the range does the same: not all particles run out of energy at the same depth, but there is an approximately gaussian spread in the distribution of the stopping point (figure 1.3, curve (b)), to which we refer as range straggling. In this latter description, we can define the range as the depth at which the beam fluence is half of its initial value.

Another phenomenon to consider, although less important, is the nuclear interaction that a particle can make at any depth, this results in a slight linear decrease of the beam intensity before reaching the stopping depth, since the beam is depleted because of the particles lost in nuclear processes.

The CSDA range R is related to the stopping power and the initial kinetic energy (E0) of the projectile particle:

R(E0) = Z E0 0  dE dx −1 dE (1.3)

Accordingly to eq. 1.3, as the kinetic energy of the primary particle increases, also the range becomes longer. The range dependence on kinetic energy follows a very simple power law, as realized by Bragg and Kleeman [6] early in the last century:

R(E0) = αE0p (1.4)

where α is a material-dependent constant and p depends on the incident particle type. The ranges of different ion with equal initial kinetic energy E per atomic mass unit and crossing the same absorber are related as follows:

R2 z2 2 m2 = R1 z2 1 m1 (1.5)

This means that, given a certain energy per unit mass, heavier ions have shorter range than lighter ones (fig. 1.4). In fact, according to eq. 1.1, the energy loss is proportional to z2_{, so they lose a greater amount of energy per path length. For instance, being equal}

the energy per nucleon, the proton range is approximately three times longer than the range of 12_{C, while protons and} 4_{He ions have same range, since the z}2_{/m ratio is the}

same.

In the field of cancer therapy, a particle beam passes through inhomogeneous tissues composed of different materials. Obtaining a good estimate of range using eq. 1.3 is not an easy task. Fortunately, there are approximations that allow us to simplify the cal-culation; one example is the Bragg-Kleeman approximation (derived from CSDA) which assumes that the mass stopping power for a compound material is [8]

1 σ  dE dx  tot =X i Wi σi  dE dx  i (1.6)

Figura 1.4: Mean range as a function of initial kinetic energy. The plot shows values related to different ions in water [7].

where Wi corresponds to the fraction of atom of the i-th element that composes the

absorbing material, σi is the density of the i-th element and σ is the overall density of

the whole absorbing medium.

Other range calculation strategies and approximations are discussed in [9].

1.1.3

Nuclear fragmentation

When an heavy charged particle travels into an absorber medium, nuclear interactions also occurs. These processes strongly depend on the energy of the incident particle: in a collision on a target nucleus, if the projectile particle energy is below the coulomb barrier, the dominant process is the Coulomb scattering, while strong interactions occurs with very low probability only through quantum tunneling effects [10]; if the energy is over the coulomb barrier, and if the impact parameter is lower than a critical value [11], the strong interaction becomes dominant. Protons and ions used in hadrontherapy have

energy between ∼ 200 - 400 MeV/u (MeV per nucleon), therefore they are allowed to make nuclear reactions and fragmentation.

The nuclear fragmentation is a nuclear collision between the projectile and the target nuclei, that leads to their destruction and to the production of other nuclei (fragments). Depending on the impact parameter2_{, this process can be divided in two categories:}

central collisions, that lead to the complete disintegration of both nuclei, resulting in a multitude of secondary fragments (dissipative processes), and peripheral collisions, that involve only a few nucleons (quasielastic processes) and that are described by the simplified abrasion-ablation model proposed by Serber [12]. In hadrontherapy, since the energie used is such as to make the second process more probable, the interest is focused on the peripheral collisions.

In case we are using protons as projectile, we have to consider that they can not fragment at therapeutic energy, the only fragmentation that occurs is the target one. In case we are using heavier ions as projectile, nuclear interactions are allowed to produce both target and projectile fragmentation.

In a peripheral collison, the fragmentation process happens in two steps, according to the Serber model. In the first stage (abrasion) nucleons are involved: they gain a certain amount of energy due to the collision and they are expelled by the target and, in the same way, some nucleons are expelled from the projectile (in the case of a Z > 1 ion). The second stage lasts about 10-18-10-16s and it is characterized by thermalization and de-excitation of the remaining nuclei that, depending on their mass and excitation energy, can happen in the following ways.

• γ-emission: the excited nucleus dissipate its residual energy by emitting photons.

• Nuclear evaporation: light fragments (Z < 2) escape from the excited residual nucleus.

• Fermi break-up: in nuclei of mass A < 16 the excitation energy can exceed the binding energy of some fragmentation channels and this cause the break of the nucleus into lighter fragments; this process is relevant in radiotherapy since A < 16 elements represent the majority of human body atoms.

• Fission: the residual nucleus breaks into two separate fragments; this process is relevant only for very heavy nuclei (usually Z > 65) that are not present in the human body in normal condition, thus it is negligible for hadrontherapy purpose. During the abrasion stage, nucleons in the overlapping region also generate the so called fireball, which evaporate during the ablation stage (figure 1.5).

Figura 1.5: A simplified model of the nuclear fragmentation due to peripheral collisions of projectile and target nucleus [13].

The secondary fragments (nucleons or ions) are emitted with velocities slightly lower than the primary particle and they are distributed within a cone of small angular aperture with respect to the direction of the incident particle. Considering the same kinetic energy, a fragment with a lower charge has a lower energy loss (according to eq. 1.1), thus it can travel a longer distance than the primaries before stopping completely. Moreover, because of the angular distribution of the emission, fragmentation also contributes to the lateral spread of the radiation. The importance of these effects increases as a function of the penetration depth and the beam energy. In other words, the reason for our interest in knowing fragmentation is that, as we will discuss later, fragments produced by the projectile3 _{can reach grater depths than the primary particles and thus release energy}

and damage the tissues beyond the Bragg peak.

The main goals of FOOT are the study of two processes: the fragmentation of the target (proton on nucleus) and the projectile fragmentation (ion on proton), since the

3_{in the laboratory frame, the projectile fragments retain much of the kinetic energy of the primary}

particle and they are emitted strongly forward, while fragments produced by the resting target are emitted with low kinetic energy.

human body can be seen as a target mainly made of hydrogen, oxygen and carbon. The reason why only nuclear processes are studied for clinical purpose, is that hadrontherapy uses beams with energies that are not high enough to produce sub-nuclear interactions (no quarks are involved). One of the problems in the fragments detection is that in peripheral collision the momentum and energy transferred are very small, because the overlap zone is small and only few nucleons interact during the collisions. So, in the case of target fragmentation is very difficult to detect the secondary products, due to their low energy they fail to escape from the target. The solution is to approach this problem with the inverse kinematic, but this part is going to be treated deeper in the next chapter.

1.2

Radiobiological considerations

1.2.1

Dosimetric quantities

Since all physical and chemical effects, and thus biological effects, induced by radia-tion are a consequence of the energy transfer from the particle to a porradia-tion of tissue, we consider the quantities that takes into account the amount of energy received by tissues. The absorbed dose (D) is defined as the energy absorbed by a mass unit of the medium.

D = dE

dm (1.7)

In the International System of Units (SI), the absorbed dose is measured in gray (Gy), corresponding to 1 J/1 kg.

Anyway, different types of radiation exist, so we should introduce the equivalent dose (H) as the product of the absorbed dose and a radiation weighting factor wR taking

into account the dangerousness of the radiation. Considering that more than one type of radiation could cross the tissue at the same time, the total equivalent dose will be the sum over the considered radiation types of the aforementioned products:

H =X

R

Radiation type Radiation weighting Factor (wr)

X-rays,γ-rays 1

Electrons, positrons 1

Neutrons continuous function of neutron energy

Protons 2

Alpha particles, fission fragments, heavy ions 20

Tabella 1.1: weighting factor of different type of radiation; the weighting factor for neutrons can range from ∼ 3 up to 20 and it is given by a continuous function of the neutron energy, as discussed in [14].

where DR is the absorbed dose related to the R-th type of radiation. Table 1.1 shows

the weighting factor wr concerning different type of radiation.

If we want to take into account the different radiosensitivity of the various organs and tissues in the human body, we must introduce another weighting factor, wT, and

define the effective dose as the sum, over all irradiated tissues T, of the products of the equivalent dose (HT, related to the T-th tissue) and the tissue weighting factor:

E =X

T

wT· HT (1.9)

Both equivalent and effective dose are dimensionally the same as absorbed dose, but, in the SI, the unit of measure is the sievert (1 Sv = 1 J/1 kg). The sievert is often used in medical physics because it can give a uniform scale to measure radiation damage regardless of the type of radiation that caused it.

1.2.2

Biological effects of radiation

Hadrontherapy and other therapies using radiation, exploit the damage that radiation causes to biological tissues in order to kill cancer cells. A cell is considered dead when its DNA has suffered such irrecoverable damage as to prevent its normal reproduction process. The genetic damage can be caused by the direct absorption of energy by DNA

(direct damage) or by the indirect action of free radicals coming from water radiolysis (indirect damge) [15].

Free radicals are atoms or molecules with an unpaired electron on the last orbital that makes them very reactive. Considering the high concentration of water in the human body, we will discuss free radicals produced by the radiolysis of water. Supposing to have an electromagnetic radiation of energy hν ionizing a water molecule, the occurring reaction is the following:

hν + H2O → H2O++ e− (1.10)

H2O + e−→ H2O− (1.11)

So we have the formation of the positive ion H2O+ and the negative ion H2O−, which

dissociate in the following way:

H2O+ → H++ OH• (1.12)

H2O− → OH−+ H• (1.13)

Thus, we have two ions (H+and OH−) and two free radicals (labelled by the • symbol) as final products, which may take part in other reactions. H+ _{and OH}− _{simply recombine}

into H2O, while possible recombination for free radicals may be the harmless reaction

H•+ OH• → H2O, (1.14)

that, again, produces water, or the reaction

OH•+ OH• → H2O2, (1.15)

that produce hydrogen peroxide, which is dangerous for the cell [16]. Thanks to enzymes and antioxidants the effects of free radicals are under control, but exogenous sources, such as particle irradiation, can increase the free radical production rate and destabilize the balancing imposed by the defense mechanisms of the cell, thus creating an oxidative damage that leads to cellular apoptosis.

We talk about direct damage when the radiation ionizes the DNA of the cell in such a way as to cause breakages in its constituent molecules. This category of damage usually splits into Single Strand Break (SSB) and Double Strand Break (DSB). A SSB occurs when the radiation breaks one of the DNA helices, leaving the other one intact. SSB is relatively easy to repair: enzymes can recover the information from the undamaged strand and make a complementary DNA segment in order to replace the damaged one. On the other hand, when a DSB occurs, both helices are broken in the same location (or in places separated by only a few base pairs), so this damage is much more difficult to repair and it is the main cause of cell death or mutations that lead to the development of neoplasms. We could also have clustered lesions when two or more lesions occur within a few tens of DNA base pairs.

1.2.3

LET and RBE

Another important dosimetric quantity is the Linear Energy Transfer (LET), which is strictly related to the stopping power and it is frequently used in radiodosimetry and radiobiology. It is defined as the amount of energy released by a radiation in the traversed material per unit length and, differently from stopping power, it does not take into account radiative energy loss (i.e. the radiative stopping power or Bremsstrahlung) or delta-rays. In fact, LET is defined as follows:

LET∆=  dE dx  ∆ (1.16)

and it is usually measured in keV/µm. In eq. 1.16, dE is the mean energy loss due to colli-sions with atomic electrons with transferred energy less than a cut-off value ∆; therefore, the cut-off value excludes secondary electrons with energies greater than δ (the symbol ∆ is usually omitted). The reason for this cut-off is to have a quantity that measures only the energy deposition close to the trajectory of the incident particle. Contrariwise, the unrestricted LET (LET∞) takes into account all possible energy transfers.

The LET varies along the incident particles track because, as the particle deposits energy in tissues, it slows down and thus the rate of delivered energy increases. In medical physics, radiations are categorized according to their LET value: ions are considered to be high LET radiations (typical values range from tens of keV/µm to hundreds of keV/µm),

whereas X-rays and γ-rays are low LET radiations (typical values are of the order of few keV/µm) due to their sparse ionizations.

Since cells response to irradiation is highly dependent on the radiation type, equal doses of different radiations may not produce the same biological response. This effect is quantified by the Relative Biological Effectiveness (RBE), which is defined as the ratio of the dose DXof a reference radiation (typically γ-rays from60Co or X-rays) to the dose

D of the radiation of interest that produces the same biological effect:

RBE = DX D     S (1.17)

where S is the survival fraction (see section 1.2.5).

Figura 1.6: RBE as a function of LET. The diagram illustrates why radiation with a LET of 100 keV/µm has the greatest RBE: for this LET, the average separation between ionizing events coincides with the diameter of the DNA double helix (i.e., about 2 nm). Radiation of this quality is most likely to produce a double-strand break from one track for a given absorbed dose [17].

The RBE depends on many physical and biological parameters, such as LET, dose rate, cell cycle phase, oxigen concentration, etc. Figure 1.6 shows the RBE dependence on LET. Since due to the high energy deposition density the radiation damage is severe, in case of high LET particles the RBE is high.

Figura 1.7: Comparison between different particles RBE curves as functions of LET [18].

In clinical practice, proton RBE is considered constant and equal to 1.1 according to ICRU recommendations [19]. Protons are therefore considered 10% more effective that photons, despite of the experimental findings. The choice to consider the proton RBE constant is due to the fact that proton LET along the track does not increase as much as for heavier ions. Other ions RBE, instead, varies significantly, e.g. up to values > 3 in case of carbon ions. In fact, the RBE increases with LET up to an ion dependent maximum value (ranging from about 100 to 200 keV/µm), reached when the distance between two subsequent interactions is comparable to the transversal dimension of DNA (∼ 2 nm), which means increasing DSB occurences, and drops as LET increases further. This fall is due to the overkilling effect: the energy deposited in a cell by a single particle is higher than the amount required to kill the cell. Thus, the further dose deposited by ions with an even higher LET is “wasted” and the RBE falls. For heavier particles, the maximum is typically shifted to a higher LET (fig. 1.7). In fact, at

the LET corresponding to the protons RBE maximum, heavier ions have broader tracks with reduced ionization density. Therefore, light particles are generally more effective than heavy particles with the same LET.

The RBE is one of the most important quantities in heavy ion treatment planning, since it determines the photon equivalent dose, usually named biological dose, obtained by multiplying the absorbed dose by RBE. The biological dose quantifies the dose of conventional radiation that would produce the same biological effect as the radiation of interest. In the past, the most used biological dose units were the Gray-Equivalent (GyE) or Gy(RBE), which is obtained by weighing the physical dose with the RBE measured in the Bragg peak.

1.2.4

Oxygen Enhancement Ratio

When a tumour grows in volume, the phenomenon of angiogenesis takes place: new blood vessels are created in order to supply oxygen to the cells in the tumour center, which are too far from the original vessels to be sufficiently oxygenated. However, often these new vessels are not generated quickly enough or they might also be defective, therefore hypoxic regions are frequent, especially in the core of large tumours.

Anyway, it has been proved that hypoxic cells are more radioresistant, because of the so called oxygen effect. This effect is quantified by the Oxygen Enhancement Ratio (OER), OER = Dhypoxis D     S (1.18)

where Dhypoxic and D are the doses resulting in the same biological or clinical effect

with hypoxic and normoxic cells respectively. S is the survival fraction described in section 1.2.5. Typically, the OER is about 3 for photons, whereas it is greatly reduced to about 1 in the case of higher LET particles [20]. This means that high LET radiation is particularly suited to treat radioresistant tumors, since they are more effective than photons at the same dose level. Figure 1.8 shows the OER value as a function of the radiation LET.

Figura 1.8: Oxygen enhancement ratio (OER) as a function of Linear Energy Transfer (LET). The vertical line (LET = 10 keV/µm) separates low-LET values from high-LET values [21].

The oxygen effect is probably related to indirect damage, in fact the presence of oxygen molecules leads to greater formation of free radicals and, consequently, to an increase in the hydrogen peroxide concentration. For this reason, in a low LET regime, hypoxic irradiated cells are less sensitive then normoxic cells. Speaking about high LET irradiation, the influence of oxygen concentration is not so much important, since the amount of hydrogen peroxide resulting from water radiolysis is generally large by itself. This happens because, as shown in figure 1.9, the ionizations along an high LET radiation track are closer than ionizations resulting from a low LET radiation, so the recombination reactions that generate hydrogen peroxide are favored.

1.2.5

Cell survival curve

Remembering the radiation damage discussed in section 1.2.2, the probability of inducing a certain type of damage, is mostly related to particle LET. In fact, the induced damage severity can be explained in terms of the different energy deposition distributions of X-rays and ions. X-rays mostly deposit energy into the cell by photoelectric effect or by Compton effect. Since the cross sections for these processes, considering the typical

Figura 1.9: ionization and free radicals formation induced by high-LET and low-LET radiations. In a high-LET regime, subsequent ionizations are separated by a distance of about 102_-103_{pm, while the formation of the H}• _{radical occurs about 15 nm away from}

the primary ionization process; in this case, the OH•+OH• recombination (that produce hydrogen peroxide) is favoured. In a low-LET regime, ionizations occur every tens of nm, thus OH•and H• couples are closer than two OH• radicals, then their recombination (that produce H2O) is favoured.

energy of photons used in radiotherapy and the typical target nuclei, are quite small (see section 1.3.4, the number of ionizations per incident photon within a cell volume is also small. Thus, many photons are required in order to deposit a significant dose and the ionization density can be assumed to be homogeneous over the entire cell volume. The spatial distribution of energy is completely different for heavy ions: charged particles have higher LET because of their higher energy deposition along their track (fig. 1.10), which results in a greater probability of causing DNA damages.

For low LET radiations the contribution of indirect DNA damages (about 65%) is larger than the direct ones (about 30%), and only ∼ 30 % of DSB are clustered, while for high LET ions, the contribution of direct hits is higher and the clustered damages rise to about 70 % [23, 24].

The different behaviour in response to photons and heavy ions can be represented by the cell survival curve (fig. 1.11): cell proliferation is analyzed after irradiation and the percentage of surviving colonies is plotted as a function of the delivered dose. The surviving fraction is the ratio between the number of surviving cells and the number of

Figura 1.10: Ionization density in a medium irradiated by X-rays (a) and high LET par-ticles (b). The small circles represent biological targets and the dots represent ionizations produced along the tracks [22]

the seeded ones, and it is conventionally plotted versus the dose on a log-linear scale. The shape of the cell survival curve depends on the type of radiation. For low-LET radiation, the curve is characterized by a shoulder region over the low dose range, while for higher doses it tends to be linear. This behavior is well described by the linear-quadratic model:

S(D) = e−αD−βD2 (1.19)

where S is the surviving fraction, D is the absorbed dose and α and β are experimentally determined parameters that measure respectively the lethal and sublethal damage suf-fered by the cell. Specifically, the βD2 _{component takes into account the natural ability}

of the cell to recover from lethal damage.

The shoulder of the survival curve is determined by the α_β ratio, that corresponds to the dose value at which the linear component (αD) and the quadratic component (βD2) are equal. The α_β ratio related to photon irradiation is used to characterize the cell type in terms of radiosensitivity: the so called late responder tissues, whose cells are

Figura 1.11: Cell survival as a function of dose for densely and sparsely ionizing radiation. The fraction of cells surviving is plotted on a logarithmic scale against dose on a linear scale [25].

characterized by low replicative activity (i.e spinal cord, cartilage, bone, lung), tend to have an high quadratic component and therefore a low α_β ratio (typically between 0.5 and 6 Gy); whereas a high ratio (typically between 7 and 20 Gy) is associated to early responder tissues, characterized by high replicative activity (i.e. skin, bone marrow, intestinal epithelium, tumor tissue). Radiosensitivity depends on the cell type and it is also influenced by the cell cycle phase [26].

As already mentioned in section 1.2.3, we can see in figure 1.12 how to extrapolate the RBE value with respect to a reference radiation. Given a fixed surviving fraction value, RBE is the ratio between the doses obtained from the two curves (the curve of the reference radiation and the curve of the radiation whose RBE we want to know). It is important to note that the RBE of a radiation is not always the same, but decreases with increasing dose.

Figura 1.12: Representation of the RBE as the ratio between dose values from different radiation given a fixed surviving fraction value. According to linear quadratic model, RBE is maximal when dose → 0. If the fractional dose increases, the RBE converges to a minimal value [27].

1.3

Treatments with heavy charged particle

1.3.1

History of hadrontherapy

Over a hundred years ago, in 1895, William Conrad R¨ontgen discovered X-rays: a mysterious radiation that today we know to be photons of energy around 104_eV.

Observing the absorption of X-rays, R¨ontgen found their extraordinary properties, as the different absorption coefficient by different tissues. This led to the first radiography. One year later, in 1896, Henry Becquerel discovered the natural radioactivity and, even if the radiobiological effects were not known at that time, the idea to cure cancer with this radiations has been achieved.

In 1931, thanks to Ernest Lawrence and Stan Livingston who realized the first cy-clotron at the University of California (Berkeley), the first application of accelerators in medicine began. Ernest and his brother John (a doctor considered the founder of nuclear medicine) started to irradiate patients with salivary gland tumor using neutron beams.

In 1946, the American physicist Robert Wilson was called to lead the team for the design and the construction of a new 160 MeV cyclotron in Harvard. He spent one year in Berkeley, collaborating with Ernest Lawrence, to complete the design of the accelerator. It was then that Lawrence asked him to define the shielding of the new cyclotron, by calculating the interactions with matter of a 100 MeV proton beam. Wilson followed this suggestion and found that protons had completely different trend with depth compared to X-rays.

Protons remove electrons from molecules, ionizing them while slowing down, and the maximum number of ionizations per millimeter occurs just before they stop. This maximum was called Bragg Peak, from the British physicist William Bragg, who was the first to observe it in alpha particles. These new knowledge allowed Wilson to propose the use of protons for irradiating solid tumors, as a better therapy than the one based on X-rays. His pioneering and now famous paper, Radiological Use of Fast Protons, was published in 1946 in the journal Radiology [28].

Two years after Wilson’s paper, researchers at the Berkeley Laboratory conducted extensive studies on proton beams and confirmed his predictions. After many animal irradiations, the first patient was treated in 1954 under the guidance of Cornelius To-bias, a Hungarian physicist, who, together with Lawrence, performed the first hadron treatment on humans. The first irradiations were not directly on the tumor but on the pituitary gland, which is responsible for making hormones that stimulate cancer cells to grow. Patients with metastatic breast cancers were treated surgically to remove most of the tumor mass and then irradiated with protons on the pituitary gland to reduce the production of grow hormones and hence the chances of metastatic proliferation. The pituitary gland was a natural site for the first treatments, because the gland location was easily identified with standard X-ray films. Between 1954 and 1974 about 1,000 hypophysis and pituitary tumors were treated with protons with a 50 % success rate.

This technique was called ’hadrontherapy’ in 1992 and this term was later used to include all types of non-conventional radiation beams used at the time: protons, helium ions, neon ions, neutrons and pions. Indeed, physicists call ’hadrons’4 _{all the particles}

that feel the strong interaction since they are made of quarks and antiquarks.

Hadrontherapy is nowadays not widely uses compared with the radiotherapy due to some practical difficulties, such as costs and the large size of the machines. In case of radiotherapy, photons are produced by accelerated electrons up to 10 MeV, while protons needs to be accelerated to reach higher kinetic energies (up to 200 MeV) in order to have a suitable range in body to reach deep sited tumors. For this reason cyclotrons and synchrotrons are used in hadrontherapy, and they are much more expensive than linear acceleretors (LINAC) which are employed in radiotherapy. Hadrontherapy is not a substitution of radiotherapy, but it is more suitable in some situations, for example, to treat tumors that are radioresistant or localized near sensitive organs.

The kind of tumors that are mostly treated with hadrontherapy are chordoma and chondrosarcoma, which are located in critical areas like the base of the cranium or spine, and uveal melanoma, for which the proton therapy produces the same chance of survival than the enucleation5. In the first two cases, after a certain time, about 80 % of patients are free from tumor recurrences, instead of the 40 % for patients treated with X-rays. For the uveal melanoma, this percentage grows up to 95 % and more than 80 % of patients also retained the sight capability after the treatment. This and more results brought lots of oncologists to approve the superiority of the proton therapy, especially for children, sice it has a lower risk of inducing carcinogenesis.

The evolution of hadrontherapy was not a process that developed only in the USA, but in the ’80s a lot of hadrontherapy centers were built also in Japan. Recently also Italy has opened 3 national centers: CATANA, in Catania, where only eye tumors are treated; CNAO, in Pavia, where since 2011 they are using both protons and carbon ions for treatments; the Proton Therapy Center, in Trento, that started to cure patients in 2014.

1.3.2

Proton therapy

Considering all the previously acquired information about Bragg curve and dosimetric quantities, we can now discuss the absorbed dose as a function of depth for a therapeutic

5_{uveal melanoma is a cancer (melanoma) of the eye involving the iris, ciliary body, or choroid}

(col-lectively referred to as the ’uvea’). Enucleation is a type of ocular surgery consisting in the removal of the eyeball, but with the eyelids and adjacent structures of the eye socket remaining.